A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand.
- Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces
- Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography
- Explores the uses of computation of iterative methods across non-linear analysis
- Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options
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- The majorization method in the Kantorovich theory
- Directional Newton methods
- Newton's method
- Generalized equations
- Gauss-Newton method
- Gauss-Newton method for convex optimization
- Proximal Gauss-Newton method
- Multistep modified Newton-Hermitian and Skew-Hermitian Splitting method
- Secant-like methods in chemistry
- Robust convergence of Newton's method for cone inclusion problem
- Gauss-Newton method for convex composite optimization
- Domain of parameters
- Newton's method for solving optimal shape design problems
- Osada method
- Newton's method to solve equations with solutions of multiplicity greater than one
- Laguerre-like method for multiple zeros
- Traub's method for multiple roots
- Shadowing lemma for operators with chaotic behavior
- Inexact two-point Newton-like methods
- Two-step Newton methods
- Introduction to complex dynamics
- Convergence and the dynamics of Chebyshev-Halley type methods
- Convergence planes of iterative methods
- Convergence and dynamics of a higher order family of iterative methods
- Convergence and dynamics of iterative methods for multiple zeros
Professor Alberto Magreñán (Department of Mathematics, Universidad Internacional de La Rioja, Spain). Magreñán has published 43 documents. He works in operator theory, computational mathematics, Iterative methods, dynamical study and computation.
Professor Ioannis Argyros (Department of Mathematical Sciences Cameron University, Lawton, OK, USA) has published 329 indexed documents and 25 books. Argyros is interested in theories of inequalities, operators, computational mathematics and iterative methods, and banach spaces.